jmac,
Great questions! I have some brief answers for you. First of all, you can visit the AADSAS website and read the instructions for applying, which will give you a good overview of the process.
This year, AADSAS-on-the-web (the easiest/quickest way to apply) was not available until June 3. Therefore, that was the *first* day to send off your application this year.
My undergrad turns out zillions of pre-dental applicants, and the school has a pre-dental committee, so getting letters of rec. was quite simple for me. My recommenders wrote letters and had them turned into the committee BY the first week of March. My committee advisor then interviewed me and put the letters together and had that completed by May 1. I had the committee send their letter to AADSAS in mid-May (about 2 weeks before the AADSAS application was available).
This process will be different for you, but I would start notifying/requesting letters of rec. from people now. It is ideal to have all of that handled and wrapped up in a nice package PRIOR to filling out AADSAS. Of course, many people are just fine doing it later, I'm just recounting what worked for me.
If you don't have a committee to gather letters for you, then you won't want your letters to be sent to AADSAS too soon. My fear was that if I had them sent too soon they would disregard them, so I tried to time it so my letters were sent to AADSAS around the time (give or take a week or two) that I would be filling out my online application.
Whichever way your school handles the letters process, begin to notify those who you want to write letters for you. You'll find that many people are slow to write letters, or extremely busy. Many professors are popular with students, and thus they are asked to write upwards of 30-40 letters a semester. Giving them advance notice will put your letter at the top of the pile, which will be of benefit to you in the long run.
Handling things early worked out really well for me, because all of the information (letters, transcripts, application) was out of my hands on June 3. From that point on, all I had to do was handle incoming secondaries and schedule interviews. My theory when applying last year was always "better early than late". Having the items in the first day also relieved me from some stress.
Good luck in the process!